For item #1, the SimBiologyModelAnalyzer app allows you to create a variant of the parameter estimates (see here for more details). After that, you can specify the variant to any simulations, or you can commit the variant to the model if you want to copy those values over to the model components. You can do something similar from the command line, but you would need to create the variant yourself. We are considering an enhancement to make these variants easier to create from the command line.
Item #2 is much harder to answer. The first thing I'd check is whether the fit program applies any other variants or doses that you may have overlooked. The next thing I'd suggest is double-checking that both simulations start with the same initial conditions. So you could update both programs to log everything, including constant parameters. Then compare the values at time=0 to make sure they are the same. If your initial conditions are all the same, then I'd compare the simulations to see where they first start to differ. If the simulations immediately start to diverge, then this suggests the dynamics are different. This usually happens because the two models implement different dynamics. But in rare cases the difference could be due to more subtle numerical issues when solving the ODEs. As a concrete example, simulations during fitting might include calculation of sensitivities that require the solver to take smaller time steps.
If you still can't figure out the source of the difference, I suggest contacting Technical Support or messaging me directly. We already have NDAs with some customers so that we can share confidential information. The SimBiology development team also has a tool that we can share to "obfuscate" your model before sharing it with MathWorks. We also sometimes set up video calls to debug things remotely.
